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  •  is a square of side 1 unit. A circle passes through vertices <img alt="\mathrm

\mathrm{A B C D} is a square of side 1 unit. A circle passes through vertices \mathrm{A, B} of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent drawn to the circle from vertex \mathrm{D} is 2 units. The radius of the circle is
 

Option: 1

\sqrt{5}


Option: 2

\frac{1}{2} \sqrt{10}


Option: 3

\frac{1}{3} \sqrt{12}


Option: 4

\sqrt{8}


Answers (1)

best_answer

Let \mathrm{A}=(0,1), \mathrm{B}=(0,0), \mathrm{C}=(1,0), \mathrm{D}=(1,1)
Family of circles passing through \mathrm{A, B}  is \mathrm{x^2+y^2-y+\lambda x=0}

\sqrt{1+\lambda}=2 \Rightarrow \lambda=3

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